Doping Dependence of Resonant spin excitations in Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$

The observation of a resonant spin excitation at $\omega $ = 14meV in Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ [Nature \textbf{456}, 930 (2008)] provided the first phase-sensitive evidence of extended $s_{\pm}$ symmetry in the iron arsenide superconductors. We will discuss subsequent measurements of the doping dependence of the dynamic magnetic susceptibility in Ba$_{1- x}$K$_{x}$Fe$_{2}$As$_{2}$ from $x$ = 0.2 to 0.9 using inelastic neutron scattering from polycrystalline samples. The resonance is observed below T$_{\mathrm{c}}$ at all values of $x$ centered on the $\Gamma$-M point at $Q \approx 1.2${\AA}$^{-1}$, but it progressively broadens and weakens in the overdoped regime. We will discuss the scaling of the resonance energy with T$_{\mathrm{c}}$ and compare the Q- dependence with theoretical estimates based on the evolution of the Fermi surface with hole doping.